The document describes methodology for estimating the channel impulse response from acoustic signals transmitted during the SAVEX15 experiment. Stationary source experiments involved transmitting chirp and m-sequence signals from a fixed source location and receiving the signals on a vertical receiver array up to 5 km away. Matched filtering of the received signals with the transmitted source signals was used to estimate the time-varying channel impulse response, which characterizes how the underwater acoustic channel responds to any input signal.
Time-Frequency Representation of Microseismic Signals using the SSTUT Technology
Resonance frequencies could provide useful information on the deformation occurring during fracturing experiments or CO2 management, complementary to the microseismic events distribution. An accurate time-frequency representation is of crucial importance to interpret the cause of resonance frequencies during microseismic experiments. The popular methods of Short-Time Fourier Transform (STFT) and wavelet analysis have limitations in representing close frequencies and dealing with fast varying instantaneous frequencies and this is often the nature of microseismic signals. The synchrosqueezing transform (SST) is a promising tool to track these resonant frequencies and provide a detailed time-frequency representation. Here we apply the synchrosqueezing transform to microseismic signals and also show its potential to general seismic signal processing applications.
Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10–15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.
Fourier Transform : Its power and Limitations – Short Time Fourier Transform – The Gabor Transform - Discrete Time Fourier Transform and filter banks – Continuous Wavelet Transform – Wavelet Transform Ideal Case – Perfect Reconstruction Filter Banks and wavelets – Recursive multi-resolution decomposition – Haar Wavelet – Daubechies Wavelet.
Time-Frequency Representation of Microseismic Signals using the SSTUT Technology
Resonance frequencies could provide useful information on the deformation occurring during fracturing experiments or CO2 management, complementary to the microseismic events distribution. An accurate time-frequency representation is of crucial importance to interpret the cause of resonance frequencies during microseismic experiments. The popular methods of Short-Time Fourier Transform (STFT) and wavelet analysis have limitations in representing close frequencies and dealing with fast varying instantaneous frequencies and this is often the nature of microseismic signals. The synchrosqueezing transform (SST) is a promising tool to track these resonant frequencies and provide a detailed time-frequency representation. Here we apply the synchrosqueezing transform to microseismic signals and also show its potential to general seismic signal processing applications.
Spectral estimation, and corresponding time-frequency representation for nonstationary signals, is a cornerstone in geophysical signal processing and interpretation. The last 10–15 years have seen the development of many new high-resolution decompositions that are often fundamentally different from Fourier and wavelet transforms. These conventional techniques, like the short-time Fourier transform and the continuous wavelet transform, show some limitations in terms of resolution (localization) due to the trade-off between time and frequency localizations and smearing due to the finite size of the time series of their template. Well-known techniques, like autoregressive methods and basis pursuit, and recently developed techniques, such as empirical mode decomposition and the synchrosqueezing transform, can achieve higher time-frequency localization due to reduced spectral smearing and leakage. We first review the theory of various established and novel techniques, pointing out their assumptions, adaptability, and expected time-frequency localization. We illustrate their performances on a provided collection of benchmark signals, including a laughing voice, a volcano tremor, a microseismic event, and a global earthquake, with the intention to provide a fair comparison of the pros and cons of each method. Finally, their outcomes are discussed and possible avenues for improvements are proposed.
Fourier Transform : Its power and Limitations – Short Time Fourier Transform – The Gabor Transform - Discrete Time Fourier Transform and filter banks – Continuous Wavelet Transform – Wavelet Transform Ideal Case – Perfect Reconstruction Filter Banks and wavelets – Recursive multi-resolution decomposition – Haar Wavelet – Daubechies Wavelet.
Short-time homomorphic wavelet estimation UT Technology
Wavelet estimation plays an important role in many seismic processes like impedance inversion, amplitude versus offset (AVO) and full waveform inversion (FWI). Statistical methods of wavelet estimation away from well control are a desirable tool to support seismic signal processing. One of these methods based on Homomorphic analysis has long intrigued as a potentially elegant solution to the wavelet estimation problem. Yet a successful implementation has proven difficult. We propose here a method based short-time homomorphic analysis which includes elements of the classical cepstrum analysis and log spectral averaging. Our proposal increases the number of segments, thus reducing estimation variances. Results show good performance on realistic synthetic examples.
- Obtained the Fast Fourier Transform of signals.
- Designed and Validated Low Pass, High Pass, and Band Pass filters in compliance with the specifications.
- Produced and compared graphs of the results upon processing.
Fundamentals of Passive and Active Sonar Technical Training Short Course SamplerJim Jenkins
This four-day course is designed for SONAR systems engineers, combat systems engineers, undersea warfare professionals, and managers who wish to enhance their understanding of passive and active SONAR or become familiar with the "big picture" if they work outside of either discipline. Each topic is presented by instructors with substantial experience at sea. Presentations are illustrated by worked numerical examples using simulated or experimental data describing actual undersea acoustic situations and geometries. Visualization of transmitted waveforms, target interactions, and detector responses is emphasized.
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
Pulse Compression Method for Radar Signal ProcessingEditor IJCATR
One fundamental issue in designing a good radar system is it’s capability to resolve two small targets that are located at
long range with very small separation between them. Pulse compression techniques are used in radar systems to avail the benefits
of large range detection capability of long duration pulse and high range resolution capability of short duration pulse. In these
techniques a long duration pulse is used which is frequency modulated before transmission and the received signal is passed through a
match filter to accumulate the energy into a short pulse. A matched filter is used for pulse compression to achieve high signal-to-noise
ratio (SNR). Two important factors to be considered for radar waveform design are range resolution and maximum range detection.
Range resolution is the ability of the radar to separate closely spaced targets and it is related to the pulse width of the waveform. The
narrower the pulse width the better is the range resolution. But, if the pulse width is decreased, the amount of energy in the pulse is
decreased and hence maximum range detection gets reduced. To overcome this problem pulse compression techniques are used in the
radar systems. In this paper, the pulse compression technique is described to resolve two small targets that are located at long
range with very small separation between them.
Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.
fast-Fourier-transform-presentation and Fourier transform for wave
in
signal possessing for
physics and
geophysics
spectra analysis
periodic and non periodic wave
data sampling
The Nyquist frequency
Short-time homomorphic wavelet estimation UT Technology
Wavelet estimation plays an important role in many seismic processes like impedance inversion, amplitude versus offset (AVO) and full waveform inversion (FWI). Statistical methods of wavelet estimation away from well control are a desirable tool to support seismic signal processing. One of these methods based on Homomorphic analysis has long intrigued as a potentially elegant solution to the wavelet estimation problem. Yet a successful implementation has proven difficult. We propose here a method based short-time homomorphic analysis which includes elements of the classical cepstrum analysis and log spectral averaging. Our proposal increases the number of segments, thus reducing estimation variances. Results show good performance on realistic synthetic examples.
- Obtained the Fast Fourier Transform of signals.
- Designed and Validated Low Pass, High Pass, and Band Pass filters in compliance with the specifications.
- Produced and compared graphs of the results upon processing.
Fundamentals of Passive and Active Sonar Technical Training Short Course SamplerJim Jenkins
This four-day course is designed for SONAR systems engineers, combat systems engineers, undersea warfare professionals, and managers who wish to enhance their understanding of passive and active SONAR or become familiar with the "big picture" if they work outside of either discipline. Each topic is presented by instructors with substantial experience at sea. Presentations are illustrated by worked numerical examples using simulated or experimental data describing actual undersea acoustic situations and geometries. Visualization of transmitted waveforms, target interactions, and detector responses is emphasized.
Sampling is a Simple method to convert analog signal into discrete Signal by using any one of its three methods
if the sampling frequency is twice or greater than twice then sampled signal can be convert back into analog signal easily......
Pulse Compression Method for Radar Signal ProcessingEditor IJCATR
One fundamental issue in designing a good radar system is it’s capability to resolve two small targets that are located at
long range with very small separation between them. Pulse compression techniques are used in radar systems to avail the benefits
of large range detection capability of long duration pulse and high range resolution capability of short duration pulse. In these
techniques a long duration pulse is used which is frequency modulated before transmission and the received signal is passed through a
match filter to accumulate the energy into a short pulse. A matched filter is used for pulse compression to achieve high signal-to-noise
ratio (SNR). Two important factors to be considered for radar waveform design are range resolution and maximum range detection.
Range resolution is the ability of the radar to separate closely spaced targets and it is related to the pulse width of the waveform. The
narrower the pulse width the better is the range resolution. But, if the pulse width is decreased, the amount of energy in the pulse is
decreased and hence maximum range detection gets reduced. To overcome this problem pulse compression techniques are used in the
radar systems. In this paper, the pulse compression technique is described to resolve two small targets that are located at long
range with very small separation between them.
Signals and Systems is an introduction to analog and digital signal processing, a topic that forms an integral part of engineering systems in many diverse areas, including seismic data processing, communications, speech processing, image processing, defense electronics, consumer electronics, and consumer products.
fast-Fourier-transform-presentation and Fourier transform for wave
in
signal possessing for
physics and
geophysics
spectra analysis
periodic and non periodic wave
data sampling
The Nyquist frequency
A signal is a pattern of variation that carry information.
Signals are represented mathematically as a function of one or more independent variable
basic concept of signals
types of signals
system concepts
Signal, Sampling and signal quantizationSamS270368
Signal sampling is the process of converting a continuous-time signal into a discrete-time signal by capturing its amplitude at regularly spaced intervals of time. This is typically done using an analog-to-digital converter (ADC). The rate at which samples are taken is called the sampling frequency, often denoted as Fs, and is measured in hertz (Hz). The Nyquist-Shannon sampling theorem states that to accurately reconstruct a signal from its samples, the sampling frequency must be at least twice the highest frequency component present in the signal (the Nyquist frequency). Sampling at a frequency below the Nyquist frequency can result in aliasing, where higher frequency components are incorrectly interpreted as lower frequency ones.
Signal and System, CT Signal DT Signal, Signal Processing(amplitude and time ...Waqas Afzal
Signal and System(definitions)
Continuous-Time Signal
Discrete-Time Signal
Signal Processing
Basic Elements of Signal Processing
Classification of Signals
Basic Signal Operations(amplitude and time scaling)
1. Methodology for channel probing
Signal processing techniques used to find the channel impulse
response from the SAVEX15 dataset
Leon Nguyen
Advisors: Heechun Song and Bill Hodgkiss
August 12, 2015
2. 1 Introduction: SAVEX15 and a signal processing primer
The Fourier transform
Signal processing
Impulse response
Why channel probe?
2 Stationary source experiments
Source signals: Chirp and m-sequence
Matched filtering to estimate the impulse response
3 Optimizing by demodulation
Complex baseband signal
Downsampling by decimation
4 Moving source experiments
Geometry of the problem and the Doppler effect
3. Introduction: SAVEX15
South
Korea
China
Japan
115°
E
120°
E 125°
E 130
°
E
135
°
E
30°
N
35°
N
40°
N
45°
N
• Shallow-water Acoustic
Variability EXperiment
• May 14-28, 2015
• Coupling of oceanography,
acoustics, and underwater
communications
• How do short- and
long-term fluctuations affect
communications
performance?
4. Introduction: SAVEX15
South
Korea
China
Japan
115°
E
120°
E 125°
E 130
°
E
135
°
E
30°
N
35°
N
40°
N
45°
N
• Shallow-water Acoustic
Variability EXperiment
• May 14-28, 2015
• Coupling of oceanography,
acoustics, and underwater
communications
• How do short- and
long-term fluctuations affect
communications
performance?
2015-08-13
Introduction: SAVEX15 and a signal processing
primer
Introduction: SAVEX15
1. Short term on the order of seconds or tens of seconds; e.g. changes
to the impulse response
2. Long term on the order of days; e.g. internal waves
5. Time-frequency analysis and the Fourier transform
Acoustic signal x(t) Time-domain representation
Fourier transform X(f ) Frequency-domain representation
The Fourier Transform and its Inverse
X(f ) =
∞
−∞
x(t)e−i2πft
dt
x(t) =
∞
−∞
X(f )ei2πft
df
Why bother with this?
• Can look at a time signal in terms of its frequency components
• Has an efficient implementation: FFT (Fast Fourier Transform)
• Preserves energy of the signal
6. Time-frequency analysis and the Fourier transform
Acoustic signal x(t) Time-domain representation
Fourier transform X(f ) Frequency-domain representation
The Fourier Transform and its Inverse
X(f ) =
∞
−∞
x(t)e−i2πft
dt
x(t) =
∞
−∞
X(f )ei2πft
df
Why bother with this?
• Can look at a time signal in terms of its frequency components
• Has an efficient implementation: FFT (Fast Fourier Transform)
• Preserves energy of the signal
2015-08-13
Introduction: SAVEX15 and a signal processing
primer
The Fourier transform
Time-frequency analysis and the Fourier
transform
1. The complex exponentials are orthogonal and form a basis for the
space of Fourier transforms. Any time signal can be written as a
linear combination of many complex exponential functions at
varying frequencies.
2. FFT reduces computation complexity from O(n2
) to O(nlogn).
3. Can be thought of as a ”rotation” to a different domain. The
magnitude squared of both domain representations are equal: total
energy across all time is equal to that across all frequencies.
Therefore, operations in one domain fully translate to the other
domain.
7. Modifying signals in the frequency domain
X(f ) =
∞
−∞
x(t)e−i2πft
dt = X(f ) eiφ(f )
• Analyze in terms of magnitude X(f ) and phase φ(f )
f
X1(f )
f
X2(f )
f
X3(f )
X1(f ) × X2(f ) = X3(f ) ⇔ x1(t) ∗ x2(t) = x3(t)
• Multiplication in the frequency domain is convolution in the
time domain
8. Modifying signals in the frequency domain
X(f ) =
∞
−∞
x(t)e−i2πft
dt = X(f ) eiφ(f )
• Analyze in terms of magnitude X(f ) and phase φ(f )
f
X1(f )
f
X2(f )
f
X3(f )
X1(f ) × X2(f ) = X3(f ) ⇔ x1(t) ∗ x2(t) = x3(t)
• Multiplication in the frequency domain is convolution in the
time domain
2015-08-13
Introduction: SAVEX15 and a signal processing
primer
Signal processing
Modifying signals in the frequency domain
1. Look at frequency-domain representation in terms of amplitude and
phase. The amplitude tells us about how much of the original signal
is present at each frequency and the phase tells us about the
position in time for each frequency.
2. If a time signal is corrupted with low-frequency noise, we can
multiply its Fourier transform with that of a high-pass filter.
9. Impulse response
Convolution
f [n] ∗ g[n] =
∞
k=−∞
f [k]g[n − k]
• Same calculation as polynomial multiplication
• E.g. [1, 1] ∗ [1, 1] → (1x + 1)(1x + 1) = 1x2
+ 2x + 1 → [1, 2, 1]
Impulse
δ[n] =
0, n = 0
1, n = 0
n
0−1 1
• Impulse response h[n] is the response
of a system to an impulse δ[n]
• Any sequence convolved with an
impulse δ[n] is itself
δ[n] ∗ h[n] = h[n]
10. Impulse response
Convolution
f [n] ∗ g[n] =
∞
k=−∞
f [k]g[n − k]
• Same calculation as polynomial multiplication
• E.g. [1, 1] ∗ [1, 1] → (1x + 1)(1x + 1) = 1x2
+ 2x + 1 → [1, 2, 1]
Impulse
δ[n] =
0, n = 0
1, n = 0
n
0−1 1
• Impulse response h[n] is the response
of a system to an impulse δ[n]
• Any sequence convolved with an
impulse δ[n] is itself
δ[n] ∗ h[n] = h[n]
2015-08-13
Introduction: SAVEX15 and a signal processing
primer
Impulse response
Impulse response
1. We switch to a discretized notation because computers work with
sampled versions of continuous/analog signals. Convolution can be
seen as a ”sliding” dot product.
2. The continuous/analog delta function is called a Dirac delta function,
which is infinitesimally short in time and infinitesimally large in
amplitude with an area of 1. The discretized version is called the
Kronecker delta function.
11. Why do we probe channels?
• If we know the impulse response h[n], we know the response
to any sampled input signal x[n]
• Can represent any x[n] as a sum of weighted and shifted
impulses δ[n]
• δ[n] ∗ h[n] = h[n]
• E.g. (0.5δ[n] + 3δ[n − 3])
input x[n]
∗ h[n] = 0.5h[n] + 3h[n − 3]
output y[n]
• The ocean is dynamic
Time Delay (ms)
Geotime(s)
0 2 4 6 8 10 12 14 16
10
20
30
40
50
Time Delay (ms)
Geotime(s)
0 2 4 6 8 10 12 14 16
10
20
30
40
50
12. Why do we probe channels?
• If we know the impulse response h[n], we know the response
to any sampled input signal x[n]
• Can represent any x[n] as a sum of weighted and shifted
impulses δ[n]
• δ[n] ∗ h[n] = h[n]
• E.g. (0.5δ[n] + 3δ[n − 3])
input x[n]
∗ h[n] = 0.5h[n] + 3h[n − 3]
output y[n]
• The ocean is dynamic
Time Delay (ms)
Geotime(s)
0 2 4 6 8 10 12 14 16
10
20
30
40
50
Time Delay (ms)
Geotime(s)
0 2 4 6 8 10 12 14 16
10
20
30
40
50
2015-08-13
Introduction: SAVEX15 and a signal processing
primer
Why channel probe?
Why do we probe channels?
1. The ocean sound channel is time-varying. The graphics show a
channel impulse response at the same location but separated in time
by 1 hour. We need frequent updates of channel impulse responses
so that the receiver can decode received communications.
2. Being able to communicate underwater allows for applications in
environmental monitoring, ocean exploration, and military
communications.
13. 1 Introduction: SAVEX15 and a signal processing primer
The Fourier transform
Signal processing
Impulse response
Why channel probe?
2 Stationary source experiments
Source signals: Chirp and m-sequence
Matched filtering to estimate the impulse response
3 Optimizing by demodulation
Complex baseband signal
Downsampling by decimation
4 Moving source experiments
Geometry of the problem and the Doppler effect
14. Stationary acoustic source experimental layout
Sta02 (VLA 1)
Sta03
Sta04 (VLA 2)
Sta05Sta06
126.1
°
E 126.2°
E
32.6
°
N
Source
• 8-element vertical array (1st
at 20 m depth)
• 7.5 m spacing
Receiver
• 16-element vertical array
(1st at 24 m depth)
• 3.75 m spacing
• 100 kHz sampling frequency
Source to Receiver Distances
Sta06 Sta03 Sta05
4.18 km 2.78 km 5.45 km
15. Stationary acoustic source experimental layout
Sta02 (VLA 1)
Sta03
Sta04 (VLA 2)
Sta05Sta06
126.1
°
E 126.2°
E
32.6
°
N
Source
• 8-element vertical array (1st
at 20 m depth)
• 7.5 m spacing
Receiver
• 16-element vertical array
(1st at 24 m depth)
• 3.75 m spacing
• 100 kHz sampling frequency
Source to Receiver Distances
Sta06 Sta03 Sta05
4.18 km 2.78 km 5.45 km
2015-08-13
Stationary source experiments
Stationary acoustic source experimental layout
1. Since the depth is only 100 m and the distances are on the order of
km, we are observing the far field case where we see the multipath
of the acoustic sound channel.
16. Source signal parameters: Chirp and m-sequence
• Source transmits 1-hour long sequence of transmissions
• 8 minutes from the hour used for each probing signal
• 1 minute for each source element
Time (ms)
Frequency(kHz)
10 20 30 40 50
0
5
10
15
20
25
30
35
40
Chirp
• Sweeps 11-31 kHz in 60 ms
• Repeats every 120 ms
m-sequence
• Pseudorandom sequence of
+1, -1 (511 digits)
• Repeats every 51.1 ms
17. Source signal parameters: Chirp and m-sequence
• Source transmits 1-hour long sequence of transmissions
• 8 minutes from the hour used for each probing signal
• 1 minute for each source element
Time (ms)
Frequency(kHz)
10 20 30 40 50
0
5
10
15
20
25
30
35
40
Chirp
• Sweeps 11-31 kHz in 60 ms
• Repeats every 120 ms
m-sequence
• Pseudorandom sequence of
+1, -1 (511 digits)
• Repeats every 51.1 ms
2015-08-13
Stationary source experiments
Source signals: Chirp and m-sequence
Source signal parameters: Chirp and
m-sequence
1. These sequences repeat periodically to fill up about 55 seconds of
the 1 minute transmission. Note that the chirp has 60 ms of silence in
between each chirp sounding.
18. Matched filtering to achieve an impulse response estimate
• Chirps and m-sequences do not model the impulse δ(t)/δ[n]
• How do we get the impulse response h[n]?
• We know: source signal s[n] and received noisy signal r[n]
r[n] = h[n] ∗ s[n]
Matched filter
y[n]
matched filter output
=
∞
k=−∞
r[k]s∗
[k − n]
• Used to detect signals in noise while achieving maximum
signal-to-noise ratio (SNR)
• Looks like convolution: y[n] = ∞
k=−∞ r[k]s[n − k]
• It is instead cross-correlation
19. Matched filtering to achieve an impulse response estimate
• Chirps and m-sequences do not model the impulse δ(t)/δ[n]
• How do we get the impulse response h[n]?
• We know: source signal s[n] and received noisy signal r[n]
r[n] = h[n] ∗ s[n]
Matched filter
y[n]
matched filter output
=
∞
k=−∞
r[k]s∗
[k − n]
• Used to detect signals in noise while achieving maximum
signal-to-noise ratio (SNR)
• Looks like convolution: y[n] = ∞
k=−∞ r[k]s[n − k]
• It is instead cross-correlation
2015-08-13
Stationary source experiments
Matched filtering to estimate the impulse response
Matched filtering to achieve an impulse
response estimate
1. The complex conjugation in one of the matched filter inputs is for
getting a positive contribution from complex signals when the
imaginary parts have the same sign. Recall i2
= −1, so we conjugate
one of the imaginary parts to get a positive contribution to the
correlation.
2. The matched filter is derived in order to attain maximum SNR.
20. Matched filtering to achieve an impulse response estimate
• Can represent matched filter output as a convolution
• We know the received noisy signal r[n] = h[n] ∗ s[n]
• s[n] ∗ s∗[−n] is the autocorrelation Rss[n] of the source signal
• Autocorrelation Rss[n] for chirp and m-sequence approximate
impulse δ[n]
y[n] =
∞
k=−∞
r[k]s∗
[k − n]
= r[n] ∗ s∗
[−n]
= h[n] ∗ s[n] ∗ s∗
[−n]
= h[n] ∗ Rss[n]
≈ h[n] ∗ δ[n] = h[n]
n
511
−1
21. Matched filtering to achieve an impulse response estimate
• Can represent matched filter output as a convolution
• We know the received noisy signal r[n] = h[n] ∗ s[n]
• s[n] ∗ s∗[−n] is the autocorrelation Rss[n] of the source signal
• Autocorrelation Rss[n] for chirp and m-sequence approximate
impulse δ[n]
y[n] =
∞
k=−∞
r[k]s∗
[k − n]
= r[n] ∗ s∗
[−n]
= h[n] ∗ s[n] ∗ s∗
[−n]
= h[n] ∗ Rss[n]
≈ h[n] ∗ δ[n] = h[n]
n
511
−1
2015-08-13
Stationary source experiments
Matched filtering to estimate the impulse response
Matched filtering to achieve an impulse
response estimate
1. The m-sequence algorithm is such that the autocorrelation will be
the length of the sequence when the sequences line up exactly and
-1 otherwise. When all of the +1 and -1 of the sequence line up
exactly, they will multiply and sum up to the length of the sequence.
Otherwise, they won’t line up and the the sum of the products cancel
out. All that remains is a -1 since the sequence does not have an
even number of +1 and -1.
2. Because of this, m-sequences are orthogonal to each other and can
be used in a MIMO system to keep track of the multiple users.
22. 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
−1
0
1
x 10
4
Time (s)
1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
−1
0
1
x 10
6
Time (s)
2.04 2.045 2.05 2.055 2.06 2.065 2.07 2.075 2.08 2.085
−1
0
1
x 10
6
Time (s)
2.04 2.045 2.05 2.055 2.06 2.065 2.07 2.075 2.08 2.085
0
5
10
x 10
5
Time (s)
23. 1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
−1
0
1
x 10
4
Time (s)
1.8 1.9 2 2.1 2.2 2.3 2.4 2.5
−1
0
1
x 10
6
Time (s)
2.04 2.045 2.05 2.055 2.06 2.065 2.07 2.075 2.08 2.085
−1
0
1
x 10
6
Time (s)
2.04 2.045 2.05 2.055 2.06 2.065 2.07 2.075 2.08 2.085
0
5
10
x 10
5
Time (s)
2015-08-13
Stationary source experiments
Matched filtering to estimate the impulse response
1. The noisy received signal r[n] is from an m-sequence. Note that the
waveform looks just like noise.
2. The matched filter output y[n] ≈ h[n] has 1074 peak detections
since the 51.1 ms m-sequence is repeated 1074 times within the 1
minute transmission. Here we only show the first 10.
3. This is a zoomed-in version of the second matched filter output. This
is the impulse response estimate from that exact point in time.
4. This is an envelope of the second matched filter output. We do this
to get a smoother output for graphical purposes because the
high-frequency components from the modulation look choppy. It is
obtained by taking the real part of the analytic signal, which gives
the baseband envelope. In MATLAB we use abs(hilbert(y)).
25. 0 2 4 6 8 10 12 14 16 18
0
2
4
6
8
x 10
5
Time Delay (ms)
MatchedFilterOutput
Time Delay (ms)
Geotime(s)
0 2 4 6 8 10 12 14 16 18
10
20
30
40
50
Time Delay (ms)
RxChannelDepth(m)
0 2 4 6 8 10 12 14 16 18
24
27.75
31.5
35.25
39
42.75
46.5
50.25
54
57.75
61.5
65.25
69
72.75
76.5
80.25
2015-08-13
Stationary source experiments
Matched filtering to estimate the impulse response
1. We stack up the 1074 envelopes to show the time-varying channel
impulse response in the bottom left. Since this represents 1 channel
from the 16 elements in the receiver array, we do the same process
for the other 15 channels and stack them all up to get the figure on
the right. Here, we can see the multipath that the sound takes at that
moment in time.
2. These graphics show a 30 dB range of matched filter output
magnitude.
26. 1 Introduction: SAVEX15 and a signal processing primer
The Fourier transform
Signal processing
Impulse response
Why channel probe?
2 Stationary source experiments
Source signals: Chirp and m-sequence
Matched filtering to estimate the impulse response
3 Optimizing by demodulation
Complex baseband signal
Downsampling by decimation
4 Moving source experiments
Geometry of the problem and the Doppler effect
27. Demodulating the passband to a baseband signal
f [kHz]
Rp[f ]
11 21 31 50
f [kHz]
Rb[f ]
10 50
• Sampling frequency 100 kHz
• Real (passband) signals are
modulated by a cosine
• m-sequence is centered at
21 kHz and has a bandwidth
of 20 kHz
• Shift passband signal to the
baseband and low-pass filter
• Centered at 0 Hz
28. Demodulating the passband to a baseband signal
f [kHz]
Rp[f ]
11 21 31 50
f [kHz]
Rb[f ]
10 50
• Sampling frequency 100 kHz
• Real (passband) signals are
modulated by a cosine
• m-sequence is centered at
21 kHz and has a bandwidth
of 20 kHz
• Shift passband signal to the
baseband and low-pass filter
• Centered at 0 Hz
2015-08-13
Optimizing by demodulation
Complex baseband signal
Demodulating the passband to a baseband
signal
1. We modulate to send signals. We occupy a high frequency band in
order to prevent low-frequency noise from interfering with our
signal. A more familiar example of modulation is FM radio, which
allows us to have multiple stations.
2. By demodulating, we get an opportunity to utilize more of the
frequency band by decimating the signal.
3. Note that negative frequencies, Nyquist theorem, and the periodicity
of the Fourier transform is not presented here.
29. Downsampling to get rid of excess data
x
y
y = sin x
x
y
y = sin 4x
f [kHz]
Rb[f ]
10 50
f [kHz]
Rd[f ]
10 12.5
• Only keep every 4th sample
• Sampling frequency and
R(f ) reduce by a factor of 4
• Low-pass filtering and
downsampling is called
decimation
• r[n]: 6 million samples to 1.5
million
• Reduces matched filtering
FFT size from 223 to 221
30. Downsampling to get rid of excess data
x
y
y = sin x
x
y
y = sin 4x
f [kHz]
Rb[f ]
10 50
f [kHz]
Rd[f ]
10 12.5
• Only keep every 4th sample
• Sampling frequency and
R(f ) reduce by a factor of 4
• Low-pass filtering and
downsampling is called
decimation
• r[n]: 6 million samples to 1.5
million
• Reduces matched filtering
FFT size from 223 to 221
2015-08-13
Optimizing by demodulation
Downsampling by decimation
Downsampling to get rid of excess data
1. The original sine wave has 40 samples to represent the period, and
the downsampled version has 10 samples.
2. Going through a 19-22 hour transmission, I was able to cut
processing time from about 2 hours to 1 hour with a downsampling
factor of 4.
31. 1 Introduction: SAVEX15 and a signal processing primer
The Fourier transform
Signal processing
Impulse response
Why channel probe?
2 Stationary source experiments
Source signals: Chirp and m-sequence
Matched filtering to estimate the impulse response
3 Optimizing by demodulation
Complex baseband signal
Downsampling by decimation
4 Moving source experiments
Geometry of the problem and the Doppler effect
32. Moving acoustic source experimental layout
Sta02 (VLA 1)
Sta04 (VLA 2)
1b
1e 1f
1a1b
1c 1h
2a
2b
2e
2f
2h
2c
3b
3a
3f
3e
126.1
°
E 126.2°
E
32.5
°
N
32.6
°
N
• Source fish towed by ship at 1.5 m/s
• Same 16-element receiver arrays from
stationary experiment
33. Moving acoustic source experimental layout
Sta02 (VLA 1)
Sta04 (VLA 2)
1b
1e 1f
1a1b
1c 1h
2a
2b
2e
2f
2h
2c
3b
3a
3f
3e
126.1
°
E 126.2°
E
32.5
°
N
32.6
°
N
• Source fish towed by ship at 1.5 m/s
• Same 16-element receiver arrays from
stationary experiment
2015-08-13
Moving source experiments
Moving acoustic source experimental layout
1. The source was at a depth of around 50 m, but ocean waves and ship
movement will cause a varying source depth in these experiments.
34. Geometry of the problem and the Doppler effect
receiver
ship velocity v
radial velocity vr
θ
• Can linearize problem around a small observation time
• Doppler effect caused by radial velocity vr = v cos θ
• Moving away from receiver causes a time dilation (+vr )
• Moving towards receiver causes a time compression (−vr )
r (t) = r((1 −
vr
c
)t)
35. Geometry of the problem and the Doppler effect
receiver
ship velocity v
radial velocity vr
θ
• Can linearize problem around a small observation time
• Doppler effect caused by radial velocity vr = v cos θ
• Moving away from receiver causes a time dilation (+vr )
• Moving towards receiver causes a time compression (−vr )
r (t) = r((1 −
vr
c
)t)
2015-08-13
Moving source experiments
Geometry of the problem and the Doppler effect
Geometry of the problem and the Doppler
effect
1. Looking at a small observation time window, θ remains almost
constant and we can linearize the Doppler effect to just the radial
velocity component. This is because the source will be kilometers
away from the receiver, and in a 30 second m-sequence transmission,
the source will only move about 45 m if the ship is moving at 1.5 m/s.
2. We have to resample the time signal to undo the effects of time
dilation/compression. This is done by interpolation, which is not
presented here.
37. 0 5 10 15 20 25 30 35 40
5
10
15
20
25
30
Time Delay (ms)
Geotime(s)
Time Delay (ms)
Geotime(s)
0 5 10 15 20 25 30 35 40
5
10
15
20
25
30
2015-08-13
Moving source experiments
Geometry of the problem and the Doppler effect
1. This channel impulse response was from when the ship was
approaching towards to receiver, starting at 6.1635 km and ending at
6.1266 km for a distance traveled of 36.9 m. The top graphic has no
Doppler effect compensation, and the bottom graphic has
compensation.
2. These graphics show a 25 dB range of matched filter output
magnitude.
38. Recap
• Impulse response allows you to know what the output will be
to any input for a linear and time-invariant system/channel
• Matched filter detects signals in noise with maximum SNR and
can be used to estimate impulse responses
• Lots of nifty signal processing tricks to speed up data
processing
Thank you for listening, and a big thanks to MPL, my advisors,
lab-mates, and fellow interns!